STDDN: A Physics-Guided Deep Learning Framework for Crowd Simulation

2026-04-03

AI Summary

Existing crowd simulation methods struggle to simultaneously satisfy macroscopic physical laws and microscopic trajectory consistency, often leading to error accumulation, poor stability, and low inference efficiency. This work proposes a neural differential equation framework that integrates the continuity equation from fluid dynamics as a physical constraint. By leveraging dynamic graph learning with density–velocity coupling, differentiable density mapping, and a cross-grid detection mechanism, the approach jointly models macroscopic density evolution and guides microscopic trajectory prediction. Evaluated on four real-world datasets in long-term simulation tasks, the method significantly outperforms state-of-the-art approaches, achieving higher accuracy while substantially reducing inference latency.

Abstract

Accurate crowd simulation is crucial for public safety management, emergency evacuation planning, and intelligent transportation systems. However, existing methods, which typically model crowds as a collection of independent individual trajectories, are limited in their ability to capture macroscopic physical laws. This microscopic approach often leads to error accumulation and compromises simulation stability. Furthermore, deep learning-driven methods tend to suffer from low inference efficiency and high computational overhead, making them impractical for large-scale, efficient simulations. To address these challenges, we propose the Spatio-Temporal Decoupled Differential Equation Network (STDDN), a novel framework that guides microscopic trajectory prediction with macroscopic physics. We innovatively introduce the continuity equation from fluid dynamics as a strong physical constraint. A Neural Ordinary Differential Equation (Neural ODE) is employed to model the macroscopic density evolution driven by individual movements, thereby physically regularizing the microscopic trajectory prediction model. We design a density-velocity coupled dynamic graph learning module to formulate the derivative of the density field within the Neural ODE, effectively mitigating error accumulation. We also propose a differentiable density mapping module to eliminate discontinuous gradients caused by discretization and introduce a cross-grid detection module to accurately model the impact of individual cross-grid movements on local density changes. The proposed STDDN method has demonstrated significantly superior simulation performance compared to state-of-the-art methods on long-term tasks across four real-world datasets, as well as a major reduction in inference latency.

Problem

• crowd simulation
• macroscopic physical laws
• error accumulation
• inference efficiency
• computational overhead

Innovation

• Physics-Guided Deep Learning
• Neural ODE
• Continuity Equation
• Crowd Simulation
• Density-Velocity Coupling